Finite Group Databasebeta

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C3×D5×Dic3⋊C4 #13086523

order1440
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23

Aliases

direct productC3×D5×Dic3⋊C4

Splittings

HallC32×C5 ⋊ C2×C4⋊C4
SylowC32 ⋊ D5×C4⋊C4
SylowC5 ⋊ C2×C3×Dic3⋊C4

Subgroups

subgroupG/H
centerC22×C3C2×D3×D5
commutatorC2×C3×C5C22×C3×C4
FrattiniC22C2×C3×D3×D5
FittingC2×C32×C4×C5C22
socleC22×C32×C5C23
prime radicalC22×C32×D5C22
cosocleC22×C3×C5C23×C3
hypercenterC2×C3×C4D3×D5
hypocenterC3×C5C2×C3×C4⋊C4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2840);